Question

A train normally takes 15 seconds
for a 2000m journey. On a particular
day, after covering 3/4th of the
distance, it's speed reduced to half of
its normal speed. How much more
time will the train take today for the
journey?​

Answer 1

Answer:

The extra time taken will be 3.75 seconds

Step-by-step explanation:

As per the data given in the question,

We have,

Distance = 2000 m = 2 km

Time taken = 15 sec = $\frac{1}{4\times60}= \frac{1}{240}$ hour

so, speed =$\frac{Distance}{time} = \frac{2\times240}{1} = 480\: km/hr$

Now, after coveing 3/4th which is 1500m, the speed is reduced to half i.e. 240km/hr.

So, time taken to cover first 1.5 km

$=\frac{1.5}{480} =\frac{1.5}{480} hour$

And time taken to cover last 0.5 km

$=\frac{0.5}{240} =\frac{1}{480}$ hour

So, total time taken this time = $\frac{1}{480} +\frac{1.5}{480} =\frac{2.5}{480} hour$

Hence, extra time taken will be= $\frac{2.5}{480} -\frac{1}{240} =\frac{2.5-2}{480} =\frac{0.5}{480} hour$= 3.75 seconds

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Answer 2

Answer:

The train will take 3.75 seconds extra to complete the journey.

Step-by-step explanation:

Total distance = 2000 m

Time taken = 15 sec

So, speed = distance/time

                 = $\frac{2000}{15}$

                 = $\frac{400}{3}$ m/s

According to the question,

Distance covered = $\frac{3}{4}$ of total distance

                              = $\frac{3}{4} \cdot 2000$

                              = $1500$ m

Time taken to cover 1500 m distance = 1500/speed

                                                               = $\frac{1500}{400/3}$

                                                               = $\frac{45}{4}$ sec

Then,

Speed reduces to half of its normal speed, i.e.,

New speed = $\frac{1}{2} \cdot \frac{400}{3}$

                   = $\frac{200}{3}$ m/s

Time taken to cover remaining 500 m distance = 500/new speed

                                                                                = $\frac{500}{200/3}$

                                                                                = $\frac{15}{2}$ sec

Total time taken to cover 2000 m distance = $\frac{45}{4}+\frac{15}{2}$

                                                                         = $\frac{45+30}{4}$

                                                                         = $\frac{75}{4}$

                                                                         = $18.75$ sec

Thus, extra time taken = $18.75-15$

                                       = $3.75$ seconds

#SPJ2